抛物型方程的Shannon小波配点法

Shannon Wavelet Collocation Method for Solving PDEs of Parabolic Type

利用Shannon小波配点法对一维抛物型方程进行求解,将一维Shannon尺度函数引入到抛物型方程求解中,选取一个适当的加窗基函数,给出了一维抛物型方程解的近似表达式,运用小波配点法对一维抛物型方程进行空间离散,将该问题转化为常微分方程组,利用龙格-库塔法对方程组进行数值求解。数值解结果显示,所采用的方法其数值解具有比较高的精度。

This paper is the use of Shannon wavelet collocation method for one-dimensional parabolic equation solving.The Shannon scaling function of one-dimensional was introduced to solve the parabolic equation.The appropriate windowed basis function was selected,and the approximation expression of one-dimensional parabolic equation was given.Furthermore,one-dimensional parabolic equation was spatially discretized by wavelet collocation method and transformed to differential equations,which could be solved by Rungc-Kutta method.The results show that the method used in this paper has a good accuracy.